sin²1°+sin²2°+.+sin²89°+sin²90°=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 01:58:08
![sin²1°+sin²2°+.+sin²89°+sin²90°=?](/uploads/image/z/1988920-64-0.jpg?t=sin%26%23178%3B1%C2%B0%2Bsin%26%23178%3B2%C2%B0%2B.%2Bsin%26%23178%3B89%C2%B0%2Bsin%26%23178%3B90%C2%B0%3D%3F)
sin²1°+sin²2°+.+sin²89°+sin²90°=?
sin²1°+sin²2°+.+sin²89°+sin²90°=?
sin²1°+sin²2°+.+sin²89°+sin²90°=?
sin²a+cos²a=1
sina=cos(90-a)
则sin89=cos1,sin88=cos2
……
所以原式=(sin²+1cos²1)+……+(sin²44+cos²44)+sin²45+sin²90
=1×44+1/2+1
=91/2
sin²1°+sin²89=1,同理类推,则原矢=45.5